Multiple calls to senior government officials and military personnel leading the operation to rescue the members of the youth soccer team rang unanswered Monday evening.
Efforts are expected to restart on Monday as low water levels in the cave have provided a brief window for a safer rescue. It takes several hours. Mr Narongsak would not say which of the boys were rescued.
An underground operations centre has been set up in the so-called "cavern 3", after which there is a further 2km journey to reach the mouth of the cave.
Meanwhile, it was also reported that Osatanakorn would be transferred to another province but continue with his role as chief of the rescue mission.
Rescuers in Thailand retrieved four of the 12 boys who have been trapped with their soccer coach in a cave for two weeks in the first phase of an operation that could take days.
In places the passage is so tight divers have to take the scuba tank off their backs and carry their gear through one piece at a time.
The boys, aged between 11 and 16, went missing with their 25-year-old coach after soccer practice on June 23, setting out on an adventure to explore the cave complex near the border with Myanmar and celebrate a boy's birthday.
The mission is seeing trained divers guide the boys and their coach to the mouth of the Tham Luang cave system through a treacherous maze of dark passageways.
Between the base camp inside the cave and the trapped boys were twisting, turning cave passageways with torrents of water gushing through.More news: Trump announces Supreme Court pick
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After a short deluge of rain on Saturday night and with more bad weather forecast, Narongsak on Sunday said authorities had to act immediately. According to the Guardian, the rescue has concluded for the night and will resume in about 10 to 20 hours.
Musk tweeted that he was working with a team from his Space X rocket company to build a "tiny kid-size submarine" to transport the boys.
Rescue operation commander Narongsak Osottanakorn told a news conference that he is very happy to see the four more boys rescued safely. If the tests are successful, the sub would be placed on a 17-hour flight to Thailand.
Rescuers and the families of the 12 boys and their football coach being saved from a Thai cave complex are "cautiously optimistic".
Expert divers have spent the past week training the boys in basic diving.
Less than an hour after the helicopter took off, Thai public television aired live video of a medivac helicopter landing close to a hospital in the city of Chiang Rai, around 60 kilometers (37 miles) from the cave.
Volunteers from as far away as Australia and the United States helped with the effort to rescue the boys.
Authorities have said the monsoons could cause water to rise in the cave.
The rescue has captured the world's attention, and many have offered their ideas on how to get the team out.